So not from a browser, but from the server, this has been answered before. I think if there were easier it would be obvious. Anders approach is the only browser way that I know how and that requires access to CA.

You might also try viewing the value of the MicrosoftSharePointTeamServices response header that SharePoint sends with every response. You can view it using the IE Dev Tools, Firebug for Firefox, Fiddler, etc.

You can also navigate to the site, click Site Actions, Site Settings and look at the Version number. You can then cross reference that figure to this list to get the product and patch level. It won't tell you if it's the free version (WSS or Foundations) or a paid for version (Standard or Enterprise) like linked by Neil.